1979 AHSME Problem 20

If a=\tfrac{1}{2} and (a+1)(b+1)=2 then the radian measure of \arctan a + \arctan b equals

\textbf{(A) }\frac{\pi}{2}\qquad \textbf{(B) }\frac{\pi}{3}\qquad \textbf{(C) }\frac{\pi}{4}\qquad \textbf{(D) }\frac{\pi}{5}\qquad \textbf{(E) }\frac{\pi}{6}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.